Potential Energies of the Orbitally Degenerate Atmospheric Rydberg Complexes

A method was developed for calculating the vibronic potential energy surfaces (PESs) of atmospheric complexes consisting of orbitally degenerate Rydberg nitrogen and oxygen molecules and the molecules of a neutral medium in the ground electronic state. The degenerate states are formed as a result of l-mixing in the D and E layers of the atmosphere during the periods of increased solar activity. The complexes are populated in the nonequilibrium two-temperature plasma and are responsible for the incoherent additional background radiation in the decimeter (microwave) and terahertz (IR) bands at an altitude of 80–110 km from the Earth’s surface. To describe the interaction of a weakly bound electron with a singly charged molecular ion and a neutral molecule of a gas medium, the formalism of the multichannel quantum defect (MCD) theory was used. Quantum-chemical calculations of the dependences of the scattering lengths, polarizabilities, and quadrupole moments of the main atmospheric molecules N₂ and O₂ on the interatomic distance were performed. The specific features of the behavior of vibronic PESs of Rydberg complexes for large values of the principal quantum number (n ? 1) were analyzed. The vibronic PESs of orbitally degenerate states were constructed. They are necessary for determining the positions and shape of the vibronic minima of the l-mixing cross sections of the N₂ and O₂ Rydberg molecules in the D and E layers of the Earth’s atmosphere, where the delay times of satellite positioning signals should be minimum. The possibility of “quantum chaos” appearing in the Rydberg complexes at sufficiently large n values and angular momenta of the weakly bound electron was noted.     

Semiempirical determination of the vibronic constants of diatomic molecules. Optimal sets of constantsa 3Σg +,e 3Σu +,d 3Πu ±, and f3Σu + of states of H2

The possibility of describing the vibronic electron levels of diatomic molecules by means of a limited set of molecular constants is investigated. For the example of the low triplet states of H₂, it is shown that, in determining the set of vibronic constants of the given electron state and their covariance matrix, account must be taken of the specific features of the physical problem for which these constants are to be used. The optimal sets of constants obtained are significantly different from those in the literature. The reasons for the discrepancy are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1986.It remain to thank N. P. Penkin, T. K. Rebane, and P. A. Braun for their interest in the work and useful discussions.     

Structural phase transition induced by the Jahn-Teller effect. Antiferrodistortive ordering

We study the phase transitions induced by the Jahn-Teller effect ofE-doublet ions in a cubic crystal with antiferrodistortive interactions. AnS=1 pseudospin model is constructed which takes the three lowest vibronic levels of the Jahn-Teller complexes into account. We find a second-order phase transition to a tetragonal phase with two inequivalent sublattices. The transitions between the vibronic levels give rise to bands of collective vibronic excitations with strongly temperature-dependent frequencies. The nature of the various modes is analyzed in detail. We also study the coupling to the elastic displacement field of the crystal. For a sufficiently large coupling constant, this coupling stabilizes a different low-temperature tetragonal phase with two equivalent sublattices. In a certain region of coupling constants, a transition occurs between the two tetragonal phases by second-order transitions to an intermediate phase of lower symmetry. The influence of the coupling on the dynamic behaviour is discussed.Supported by Schweizerischer Nationalfonds     

Structural phase transition induced by the Jahn-Teller effect. Antiferrodistortive ordering

We study the phase transitions induced by the Jahn-Teller effect ofE-doublet ions in a cubic crystal with antiferrodistortive interactions. AnS=1 pseudospin model is constructed which takes the three lowest vibronic levels of the Jahn-Teller complexes into account. We find a second-order phase transition to a tetragonal phase with two inequivalent sublattices. The transitions between the vibronic levels give rise to bands of collective vibronic excitations with strongly temperature-dependent frequencies. The nature of the various modes is analyzed in detail. We also study the coupling to the elastic displacement field of the crystal. For a sufficiently large coupling constant, this coupling stabilizes a different low-temperature tetragonal phase with two equivalent sublattices. In a certain region of coupling constants, a transition occurs between the two tetragonal phases by second-order transitions to an intermediate phase of lower symmetry. The influence of the coupling on the dynamic behaviour is discussed.     

The C-N Stretching Vibronic Bands of the MgNC ÃΠ-X?Σ Transition

We have generated MgNC in supersonic free jet expansions and measured the laser-induced fluorescence excitation spectra of the C-N stretching vibronic bands of the òΠ-X?²Σ⁺ transition. Rotational analysis yields the molecular constants of the vibronic levels, (1,0,0) and (1,0,1), in the Ã²Π state. We cannot find any anomalies in the constants of these vibronic levels, while they are predicted to lie above the barrier of the isomerization reaction pathway, MgNC↔MgCN, on the Ã²Π state. On the basis of the molecular constants obtained, we discuss the fine structures of both the ground X?²Σ⁺ and excited Ã²Π states.     

Coriolis coupling in degenerate vibronic states of spherical top molecules

The first-order contribution of coriolis coupling to the rotational energies of degenerate vibronic states of spherical top molecules is considered for both even and odd numbers of electrons in octahedral or tetrahedral molecules. For E vibronic states the contribution vanishes, while for F ₁, F ₂, E _1/2 and E _5/2 states simple formulae are given. For G _3/2 states the energies are in general complicated, but simple formulae are given for two limiting cases.     

Electronic structure of semiconductor quantum dots: Interband transitions and selection rules

The energy spectrum and bound-bound interband transitions in semiconductor quantum dots are analysed within the effective mass approach. Interband bound-bound transition intensities are calculated and it is shown that the conventional l=const selection rule is slightly lifted when the refractive index nonuniformity of the structure is taken into account. Specifically, numerical calculations for a GaAs dot in Al_xGa_1−xAs matrix indicate that, along with fullyallowed transitions, some of l-nonconserving transitions may be detectable, as well.     

A symmetry-based approach to the effective Hamiltonian for symmetric top molecules in degenerate vibronic states

The effective Hamiltonian for a symmetric top molecule in a degenerate vibronic state is obtained. Included in this Hamiltonian are the rotational, spin-rotational, spin-orbit coupling and electronic spin-spin interactions. The terms of the Hamiltonian are expressed as the product of molecular ‘constants,’ rotational angular momentum operators, and symmetry operators. A formalism is derived, and tables included, to determine whether or not a symmetry operator vanishes for a given vibronic state of a particular molecular symmetry. In this way, one can easily obtain all the non-vanishing Hamiltonian terms for a particular application.     

Electron resonance studies of the renner effect

The gas phase electron resonance spectra of NCO in its ground ²Π_3/2 vibronic state and in two excited vibronic states are described. Theoretical analysis of the spectra yields effective g values for the three states. In additon the ¹⁴N magnetic hyperfine and electric quadrupole coupling constants and the electric dipole moment are determined. The theory of the Renner coupling of electronic and vibrational motion is extended, and shown to account for anomalous contributions to the g values. The theory also shows that these contributions are closely related to the Renner coupling constant.     

Effects of vibrational intercentre interaction in a trigonal two-centre system with twofold electronic degeneracy at each centre

The effect of intercentre interaction (via vibrations and electron-electron coupling) on the magnetic and magnetic resonance characteristics of a pair of Jahn-Teller centres is investigated. In the limiting case of strong vibronic coupling when the splitting of degenerate electronic terms is sufficiently large the exchange Hamiltonian for the pair has the Heisenberg form. The energy spectrum of spin states of the pair system is obtained and the temperature dependence of the effective magnetic moment is investigated. It is shown that under some conditions this temperature dependence has an anomalous nonmonotonic character. The g factors of the two-centre Jahn-Teller system are obtained and the changes of the EPR spectrum with the exchange and vibrational coupling constants is analysed. With inclusion of only the exchange interaction, the pair spectrum possesses an additional isotropic resonance placed in the middle of the known broadened EPR spectrum of single centres with the Jahn-Teller effect for an orbital E term. The vibrational interaction between the centres results in a radical transformation of the spectrum, which in this case contains only an isotropic resonance line.     

Electronic and electron-phonon phenomena in low-dimensional BEDT-TTF-based organic conductors and superconductors

Two related groups of k-phase ion-radical salts (BEDT-TTF) with different electrical properties, namely, superconductors with different transition temperatures and conductors, which transfer to insulating state with decreasing temperature, have been studied by micro-optic spectroscopy. Polarized reflectance spectra of microcrystals have been measured for the three principal crystallographic directions within the 700–40000 cm⁻¹ region, and the corresponding spectra of the optical functions obtained. The anisotropy of the electronic system in the crystals has been established as two-dimensional. The spectra obtained were quantitatively analyzed, the key parameters of the electronic structure and the vibronic coupling constants determined. It is concluded that the conductors have smaller vibronic coupling constants, more narrow allowed electronic bands, and stronger electron-electron interaction compared to those of the superconductors, and that vibronic coupling is the necessary condition for the onset of superconductivity in the superconductors studied. Fiz. Tverd. Tela (St. Petersburg) 41, 897–899 (May 1999)     

Infrared Transitions of HCN and HCN between 500 and 10 000 cm

We have measured the Fourier transform spectrum (FTS) of two isotopomers of hydrogen cyanide (H¹²C¹⁴N and H¹²C¹⁵N) from 500 to 10 000 cm⁻¹. The infrared data have been combined with earlier published microwave and submillimeter-wave measurements. From this analysis new vibration–rotation energy levels and constants are given, based on the observation of a number of new vibrational levels, especially for H¹²C¹⁵N. The Coriolis interaction involving Δv₃= −1, Δv₂= 3, and Δl= ±1 has been observed for a great many levels and in some cases the assignments of laser transitions allowed by this interaction are more clearly shown. New vibration–rotation constants are given that allow one to predict the transition wavenumbers for most of the transitions below 10 000 cm⁻¹with accuracies of about 0.5 cm⁻¹or better. Values are given for the power series expansion of thel-type resonance constants and for the centrifugal distortion constants, as well as the usual vibrational and rotational constants.     

等离子体屏蔽效应对类氢离子能级结构和辐射跃迁性质的影响

在Debye-Hückel屏蔽近似下,基于相对论Dirac-Fock方法,发展了包括等离子体屏蔽效应的自洽场计算程序.使用该程序研究了等离子体屏蔽效应对类氢离子能级结构和辐射跃迁性质的影响.结果表明,当原子处于等离子体环境中,所有束缚态能级向连续态移动, 移动量随着屏蔽长度的减小而增大.振子强度随屏蔽长度的变化也表现出了相同的规律.进一步分析了相对论效应和等离子体屏蔽效应的耦合,发现对于中Z元素,相对论效应和等离子体屏蔽效应存在较强的耦合.讨论了等离子体屏蔽效应对原子精细结构能级的影响.计算发现,由于等离子体屏蔽效应,原子的能级次序发生了变化,κ简并被消除. 关键词： 等离子体屏蔽 Debye-Hückel 模型 能级结构 跃迁概率     

Intramolecular excitation transfer. The lowest n→π* transitions in pyrazine

In the pyrazine molecule, which has filled non-bonding orbitals para to each other, two orbitally degenerate n→π* transitions are expected, one symmetry forbidden and one symmetry allowed. Interelectronic interactions remove this degeneracy. The lowest pair of (n, π*) triplet states and the corresponding pair of singlet states are studied with a view towards determining the magnitude of such interactions and the ordering of the forbidden and allowed components. Absorption spectra are obtained of pyrazine in crystalline hydrogen and rare gases at 4·2°k, of pure crystalline pyrazine at 4·2°k, and of 42 metres of pyrazine vapour at various pressures. The phosphorescence spectrum of pyrazine in crystalline rare gases at 4·2°k also is studied. The splitting between the two singlet components is found to be approximately 435 cm^?1 with the forbidden component lying lowest. The forbidden singlet-singlet transition gains some of its intensity through vibronic mixing with a (π, π*) state, but vibronic coupling between the two (n, π*) states also may be present. The strongest part of the singlet-triplet absorption spectrum is found to involve the same upper state as the phosphorescence spectrum, and the transition is shown to be symmetry allowed. It is strongly suggested that the ordering of the allowed and forbidden components of the triplet state is inverted from that of the singlet, or the two states may lie very close together. Using an ‘independent systems’ model, a calculation of the splitting, with the inclusion of exchange is made. The theory indicates that the singlet states are indeed split by a coulomb term having roughly the expected magnitude with the forbidden component lying lowest; in addition, there is a very small exchange term with the opposite sign. The splitting between the triplets is shown to involve only the small exchange term, and the order of the allowed and forbidden components becomes reversed. There is no indication of pyrazine fluorescence at 4·2°k in any of the solids used. This fact illustrates the high efficiency of the singlet-triplet radiationless process even under these conditions where the rate might be expected to be a minimum for condensed phases. An interesting alternation of spacing has been discovered in the first few quantum levels of the 600 cm^?1 a _1g ring-bending vibration of the ground electronic state of the molecule.     

Symmetries of Type D Pure Radiation Fields

The geometrical symmetries corresponding to the continuous groups of collineations and motions generated by a null vector l are considered. These symmetries have been translated into the language of Newman-Penrose formalism for pure radiation (PR) type D fields. It is seen that for such fields, conformal, special conformal and homothetic motions degenerate to motion. The concept of free curvature, matter curvature and matter affine collineations have been introduced and the conditions under which PR type D fields admit such collineations have been obtained. Moreover, it is shown that the projective collineation degenerate to matter affine, special projective, conformal, special conformal, null geodesic and special null geodesic collineations. It is also seen that type D pure radiation fields admit Maxwell collineation along the propagation vector l.     

Anharmonic corrections for linear triatomic molecules subject to the Rennet-Teller effect

The effects of vibrational anharmonic terms and of the g_K -correction on the energy levels of a triatomic molecule in a degenerate electronic state are considered. The electronic wavefunctions are described using the approach first suggested in the original paper of Renner. Formulae for the anharmonic corrections in a number of different situations are derived. For an electronic Π state the corrections are given in the form where i runs over the various contributions and x ₁, x ₂, … depend on the anharmonic force constants. The functions F_i can be determined numerically (see equations (4.3) and 4.7)). For the case without spin-orbit interaction the F_i s are given explicitly to first order in ∈ in table 1. Further-more, the same results apply for levels with |K|=v ₂+1 even if the spinorbit interaction is not negligible. Explicit results for levels with |K|<v ₂ including spin-orbit interaction are given in tables 2 and 3. The cases with larger values for Λ (2, 3, …) are also considered. The energy level formulae for a Δ state differ from those derived earlier by Merer and Travis. In particular, the small separation between the vibronic Φ and Π levels with v ₂=1 is now found to be 4g_K . The additional terms that arise from end-over-end rotation of the molecule are discussed in § 6.     

High-Resolution Infrared Spectra of the ν2, ν3, ν4, and 2ν3 Bands of SO3

New measurements are reported for the infrared spectrum of sulfur trioxide, ³²S¹⁶O₃, with resolutions ranging from 0.0015 cm⁻¹ to 0.0025 cm⁻¹. Rovibrational constants have been measured for the fundamentals ν₂, ν₃, and ν₄ and the overtone band 2ν₃. Comparisons are made with the earlier high-resolution measurements on SO₃, and the high correlation among some of the constants related to the Coriolis coupling of the ν₂ and ν₄ levels is discussed in order to understand the areas of disagreement with the earlier work. Splittings of some of the levels are observed and the splitting constant for K=3 of the ground state is determined for the first time. Other observed splittings include the K=1 levels of 2ν₃ (l=2), the K=2 levels of ν₃ and ν₄, and the K=3 levels of ν₂. The analysis shows that there are level crossings between the l=0 and l=2 states of 2ν₃ that allow one to determine the separation of the subband centers for these two states even though access to the l=0 state from the ground state is electric-dipole forbidden. This is a generalized phenomenon that should be found for many other molecules with the same symmetry. The l-type resonance constant, q₃, that causes the splitting of the l₃=±1, k=±1 levels of ν₃ also couples the l₃=0 and 2 states of 2ν₃.     

Fully rotationally resolved ZEKE photoelectron spectroscopy of C6H6 and C6D6: photoionization dynamics and geometry of the benzene cation

A comprehensive set of spectra for the benzene cation and the perdeuterated benzene cation has been recorded with full rotational resolution using zero kinetic energy photoelectron spectroscopy (ZEKE) at high resolution (up to 0.2 cm^?1), using a slow-rising extraction pulse. With different rovibronic levels in the S₁ 6^l state as intermediate resonance, the rotational transitions to the vibronic ground state of the cation have been recorded using two-colour, two-photon resonance enhanced multiphoton ionization. A simple spectator model has been employed to simulate the intensities of the ZEKE transitions. By fitting the simulations to the recorded spectra, improved values for the rotational constants and the Coriolis coupling parameters of benzene and perdeuterated benzene have been obtained. The CC and CH bond lengths of the cation have been deduced. The spectator model is shown to be reliable despite the fact that no specific allowance is made for the effect of final state interactions on the signal intensity.     

An ab initio study of the hyperfine structure in the X2 Π electronic state of HCCS–calculation of vibronically averaged components of the anizotropic hyperfine tensor

The results of ab initio calculations of the vibronically averaged components of the anisotropic magnetic hyperfine tensor in the low-lying vibronic species of the X²Π electronic state of the HCCS radical are reported. The electronically averaged hyperfine coupling constants for hydrogen, deuterium, ¹³C and ³³S are obtained as functions of two bending vibrational modes by the density functional theory method. The vibronic wave functions are calculated with the help of a variational approach which takes into account the Renner–Teller effect and spin-orbit coupling. The results of ab initio calculations are compared to the corresponding experimental findings.     

Detecting non-Abelian geometric phases with superconducting nanocircuits

We propose a feasible scheme to detect the noncommutative feature of non-Abelian geometric phases (NAGP) with superconducting nanocircuits. The induced NAGP associated with two-fold degenerate states naturally arises in the chosen four-level subsystem interacting with the microwave pulses. We explicitly show the noncommutative effect of the NAGP by considering the difference between the level populations at the end of the composed evolution loops l₂l₁ and the counter-ordered one l₁l₂. The scheme opens the new possibility for detecting the fundamental characteristics of the NAGP with superconducting circuit devices.